F/M Ratio | Activated Sludge Process | Wastewater Treatment Plant

F/M Ratio

The F/M ratio is the ratio of the pounds of BOD5 applied to the reactor per day per pound of suspended solids (the microbial mass) in the aeration basin liquid, known as the “mixed liquor.”

This then is the pounds of BOD5 applied to the reactor per day per pound of mixed liquor suspended solids (MLSS). This ratio is also sometimes calculated using the same symbols, but using the mixed liquor volatile suspended solids (MLVSS). This calculation is used because there is a significant school of thought that points out that only the organic solids are subject to biological degradation and that the volatile suspended solids represent the organic fraction. Therefore, using the MLVSS for this calculation, rather than the MLSS, provides a more realistic value of the actual F/M ratio. In those cases where the fixed suspended solids, or the inorganic fraction of the suspended solids, are abnormally high, this may be true. For most applications, however, the high variability of the influent wastewater characteristics is sufficient to render this refinement of limited value, particularly since most treatment plants maintain a consistent MLVSS:MLSS ratio. The F/M ratio is the key control parameter for operation of the activated sludge system, however, and must be calculated carefully.

F/M = [(Q) (BOD5)]/[(V) (MLSS)]

Where:

F/M = Food to microorganism ratio in pounds of BOD5 applied per day per pound of MLSS (kilograms of BOD5 applied per day per kilogram of MLSS)

Q = Wastewater flow rate in millions of gallons per day (cubic meters per day)

BOD5 = Concentration of BOD5 in the influent wastewater in mg/L (grams/m3)

V = Liquid volume in the aeration basin in millions of gallons (cubic meters)

MLSS = Mixed liquor suspended solids concentration in mg/L (grams/m3)

There is a direct, inverse, relationship between the F/M ratio and the parameters of BOD5 loading per unit volume per day and the aeration period. If the aeration period is changed, the BOD5 loading is also changed in inverse proportion. If the aeration period is cut in half, for example, the BOD5 loading per unit volume per day is doubled for the same BOD5 concentration in the wastewater. On the other hand, the F/M ratio expresses the BOD5 concentration as a function of the growth rate and concentration of the microbes in the reactor rather than as a function of the reactor volume. That means that the F/M ratio is not a function of either the basin volume or the aeration period. Thus, two different reactors, treating a wastewater with the same influent BOD5 concentration but using very different aeration periods and reactor volumes, can have identical F/M ratios. A shorter aeration period with a higher MLSS concentration will yield the same F/M ratio as a longer aeration period with a lower MLSS concentration in a conventional activated sludge treatment plant.